Real Madrid have been heavily linked with the Croatian international this summer but have yet to strike a deal with Spurs who will stand firm on their £40 million valuation.
The midfield playmaker was reprimanded for missed training last week and was left at home as the North London club jetted off to the United States for their pre-season tour.
The 26-year-old is keen to secure a move to the Spanish champions with Villas-Boas and chairman Daniel Levy reportedly prepared to let him leave before his behavour disrupts their preparations for the new Premier League campaign.
Paris Saint Germain, Chelsea and Manchester United are also monitoring the situation in Modric but he will on the books at White Hart Lane until any of the interested parties are willing match the price tag on his head.
“There is no news at the moment,” said Villas-Boas.
“The player is training in London. There have been no further bids, no improved bids. The value hasn’t been met for what we think is correct.
“We have a big squad and we are fielded in most of the positions, so we just have to wait and see how that deal goes or doesn’t go.
“If the player eventually stays, he is a player of fantastic talent for us and will certainly add to our squad.”
It’s rumoured that Madrid chief Jose Mourinho has made a personal plea to Levy, renowned for his staunch negotiating practice, to allow Modric to make the switch to the Santiago Bernabeu.
Mourinho is becoming increasingly frustrated that his primary transfer target has yet to be captured and now wants him in place before his side travel to play LA Galaxy in America next Thursday.